2026-08-17T07:22:29Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/647182023-08-25T23:02:46Zcom_20.500.14352_14col_20.500.14352_15

3-variétes qui ne sont pas des revêtements cycliques ramifiés sur S3 Montesinos Amilibia, José María Let M denote a p-fold, branched, cyclic, covering space of S3, and suppose that the three-dimensional Smith conjecture is true for p-periodic autohomeomorphisms of S3. J. S. Birman and H. M. Hilden have constructed an algorithm for deciding whether M is homeomorphic to S3 [Bull. Amer. Math. Soc. 79 (1973), 1006–1010]. Now every closed, orientable three-manifold is a three-fold covering space of S3 branched over a knot [Hilden, ibid. 80 (1974), 1243–1244], but, in the present paper, the author shows that, if Fg is a closed, orientable surface of genus g≥1, then Fg×S1 is not a p-fold, branched cyclic covering space of S3 for any p. As the author points out, this was previously known for p=2 [R. H. Fox, Mat. Hisp.-Amer. (4) 32 (1972), 158–166; the author, Bol. Soc. Mat. Mexicana (2) 18 (1973), 1–32]. 2023-06-21T02:03:05Z 2023-06-21T02:03:05Z 1975 journal article 0002-9939 10.1090/S0002-9939-1975-0353293-9 https://hdl.handle.net/20.500.14352/64718 http://www.ams.org/journals/proc/1975-047-02/S0002-9939-1975-0353293-9/S0002-9939-1975-0353293-9.pdf http://www.ams.org/ fra restricted access American Mathematical Society